The aim of this paper is to establish the close connection between prime ideals and torsion theories in a non necessarily commutative noetherian ring. We introduce a new definition of support of a module and characterize some kinds of torsion theories in terms of prime ideals. Using the machinery introduced before, we prove a version of the Mayer-Vietoris Theorem for local cohomology and establish a relationship between the classical dimension and the vanishing of the groups of local cohomology on a classical ring.
@article{urn:eudml:doc:41723,
title = {Local cohomology in classical rings.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {427-437},
mrnumber = {MR1209813},
zbl = {0782.16023},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41723}
}
Bueso Montero, José Luis; Jara Martínez, Pascual. Local cohomology in classical rings.. Publicacions Matemàtiques, Tome 36 (1992) pp. 427-437. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41723/